$\vec u = 6\hat i +7\hat j$ Find the direction angle of $\vec u$. Enter your answer as an angle in degrees between $0 ^\circ$ and $360^\circ$ rounded to the nearest hundredth. $\theta =$
What is a direction angle? The direction angle, $\theta$, of $\vec{u}$ is the angle between the positive $x$ -axis and $\vec{u}$. $y$ $x$ $(6, 7)$ $\vec u$ $\theta$ Using the inverse tangent function Let's think about the components of $\vec u$ and use the inverse tangent function, $\tan^{-1}$ (also sometimes called arctangent and written as $\arctan$ or $\text{atan}$ ) to find $\theta$. $y$ $x$ $(6, 7)$ $\vec u$ $\theta$ $7}$ $6}$ $\theta = \text{tan}^{-1} \left ( \dfrac{\text{Vertical component}}{\text{Horizontal component}} \right) ~~~$ $\theta=\text{tan}^{-1}\left(\dfrac{7}{6}\right)$ $\theta\approx{49.4^\circ}$ This makes sense because ${49.4^\circ}$ is in the first quadrant, and $\vec u$ is in the first quadrant. The answer $\theta \approx 49.4^\circ$